When you complete Steam's registration process, you create a Steam account ("Account"). Your Account may also include billing information you provide to us for the purchase of Subscriptions. You are solely responsible for all activity on your Account and for the security of your computer system. You may not reveal, share or otherwise allow others to use your password or Account. You agree that you are personally responsible for the use of your password and Account and for all of the communication and activity on Steam that results from use of your login name and password. You may not sell or charge others for the right to use your Account, or otherwise transfer your Account.

Is there an option to hand over my property/library if I cease to exist?

This.. this is more something you should contact support about. Even though the SSA clearly states no distribution of your steam account for profiting purposes or to give to someone else not related to family bloodlines. I am not sure how it covers giving it in a will. Chances are it makes no difference.

Nope, only the creator of the account "owns" the account, accounts can't be transferred in any way, if you do, and Valve notice it, they will lock the account.

In short, the account dies with you.

My point it, given the case of your eventual demise, Valve couldn't prove that someone else took over that account unless someone registered a complaint about it. Changing your nickname, avatar, description, facebook account, credit card, email address, etc is all stuff that is easy to do and allowed in Steam. There is nothing on my Steam account that links specifically back to me other than the keys of a few games I purchased at retail, my email address, and my credit card information.

Nope, only the creator of the account "owns" the account, accounts can't be transferred in any way, if you do, and Valve notice it, they will lock the account.

In short, the account dies with you.

Do you seriously think anyone follows that link of thinking?
As someone else mentioned above, local laws supersede Valves SSA, so passing an account down in a will to a family member is allowed. Besides, how is Valve going to "find out" you gave an account to your son/daughter? Why would they care? I have never heard of anyone getting banned from letting a family member use their account.

Personally, I would never let my account "die with me". That would be silly and a waste.

Steam has indicated that family members playing on the same account is ok. They don't want to prohibit legitimate uses like that, or the transfer of your account to your next of kin, or whoever you want to give it to in that kind of unfortunate event. What that clause is designed to deter is commercial enterprises taht are based on selling Steam game libraries to other users.

I am jealous of anyone who has enough time to worry about who will get the game collection when they die. I have real life actual problems that need solving. Having a hard time taking this thread serious as a result. Beside the answer to this question is so obvious it is impossible to not know and has already be answered, don't ask don't tell. It is so obvious I question your motive for starting such a thread.